Modeling and simulation of conditionally volume averaged viscoelastic two-phase flows

Conditional volume averaging is used to develop a model capable of simulating two‐phase flows of viscoelastic fluids with surface tension effects. The study is started with the single‐phase mass and momentum balances, which are subsequently conditionally volume averaged. In doing so, we arrive at a set of equations having unclosed interfacial terms, for which closure relations for viscoelastic fluids are presented. The resulting equations possess a structure similar to the single‐phase equations; however, separate conservation equations are solved for each phase. As a result, each phase has its own pressure and velocity over the entire domain. Next, our numerical implementation is briefly outlined. We find that a Poiseuille single‐phase flow is predicted correctly. The closure terms are examined by considering a two‐phase shearing flow and a quiescient cylinder with surface tension. A convergence analysis is performed for a steady stratified two‐phase flow with both phases being viscoelastic. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3914–3927, 2013